SOLUTION: The expression ax�+bx+c is divisible by (x-1),has remainder 2 when divided by (x+1) and remainder 6 when divided by (x-2).Find the values of a, b and c.

Question 1108049: The expression ax�+bx+c is divisible by (x-1),has remainder 2 when divided by (x+1) and remainder 6 when divided by (x-2).Find the values of a, b and c.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Remainder theorem
divisible by x-1 with no remainder means f(1)=0
a+b+c=0
similarly a(-1)^2+b(-1)+c=2
a-b+c=2
and a(2^2)+b(2)+c=6
4a+2b+c=6
add the first two and b disappears
2a+2c=2; a+c=1, c=1-a
substitute into the third
4a+2b+1-a=6
3a+2b=5
substitute into the second
a-b+(1-a)=2
b=-1
therefore, a=(7/3) b=-1 and c must equal -(4/3) ANSWER
(7/3)x^2-x-(4/3) is the expression

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